{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Describing function analysis\n",
    "Richard M. Murray, 27 Jan 2021\n",
    "\n",
    "This Jupyter notebook shows how to use the `descfcn` module of the Python Control Toolbox to perform describing function analysis of a nonlinear system.  A brief introduction to describing functions can be found in [Feedback Systems](https://fbsbook.org), Section 10.5 (Generalized Notions of Gain and Phase)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import control as ct\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Built-in describing functions\n",
    "The Python Control Toobox has a number of built-in functions that provide describing functions for some standard nonlinearities. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Saturation nonlinearity\n",
    "\n",
    "A saturation nonlinearity can be obtained using the `ct.saturation_nonlinearity` function.  This function takes the saturation level as an argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "saturation=ct.saturation_nonlinearity(0.75)\n",
    "x = np.linspace(-2, 2, 50)\n",
    "plt.plot(x, saturation(x))\n",
    "plt.xlabel(\"Input, x\")\n",
    "plt.ylabel(\"Output, y = sat(x)\")\n",
    "plt.title(\"Input/output map for a saturation nonlinearity\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "amp_range = np.linspace(0, 2, 50)\n",
    "plt.plot(amp_range, ct.describing_function(saturation, amp_range).real)\n",
    "plt.xlabel(\"Amplitude A\")\n",
    "plt.ylabel(\"Describing function, N(A)\")\n",
    "plt.title(\"Describing function for a saturation nonlinearity\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backlash nonlinearity\n",
    "A friction-dominated backlash nonlinearity can be obtained using the `ct.friction_backlash_nonlinearity` function.  This function takes as is argument the size of the backlash region."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "backlash = ct.friction_backlash_nonlinearity(0.5)\n",
    "theta = np.linspace(0, 2*np.pi, 50)\n",
    "x = np.sin(theta)\n",
    "plt.plot(x, [backlash(z) for z in x])\n",
    "plt.xlabel(\"Input, x\")\n",
    "plt.ylabel(\"Output, y = backlash(x)\")\n",
    "plt.title(\"Input/output map for a friction-dominated backlash nonlinearity\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "amp_range = np.linspace(0, 2, 50)\n",
    "N_a = ct.describing_function(backlash, amp_range)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(amp_range, abs(N_a))\n",
    "plt.xlabel(\"Amplitude A\")\n",
    "plt.ylabel(\"Amplitude of describing function, N(A)\")\n",
    "plt.title(\"Describing function for a backlash nonlinearity\")\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(amp_range, np.angle(N_a))\n",
    "plt.xlabel(\"Amplitude A\")\n",
    "plt.ylabel(\"Phase of describing function, N(A)\")\n",
    "plt.title(\"Describing function for a backlash nonlinearity\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### User-defined, static nonlinearities\n",
    "\n",
    "In addition to pre-defined nonlinearies, it is possible to computing describing functions for static nonlinearities.  The describing function for any suitable nonlinear function can be computed numerically using the `describing_function` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define a saturation nonlinearity as a simple function\n",
    "def my_saturation(x):\n",
    "    if abs(x) >= 1:\n",
    "        return math.copysign(1, x)\n",
    "    else:\n",
    "        return x\n",
    "\n",
    "amp_range = np.linspace(0, 2, 50)\n",
    "plt.plot(amp_range, ct.describing_function(my_saturation, amp_range).real)\n",
    "plt.xlabel(\"Amplitude A\")\n",
    "plt.ylabel(\"Describing function, N(A)\")\n",
    "plt.title(\"Describing function for a saturation nonlinearity\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stability analysis using describing functions\n",
    "Describing functions can be used to assess stability of closed loop systems consisting of a linear system and a static nonlinear using a Nyquist plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Limit cycle position for a third order system with saturation nonlinearity\n",
    "\n",
    "Consider a nonlinear feedback system consisting of a third-order linear system with transfer function $H(s)$ and a saturation nonlinearity having describing function $N(a)$.  Stability can be assessed by looking for points at which \n",
    "\n",
    "$$\n",
    "H(j\\omega) N(a) = -1$$\n",
    "\n",
    "The `describing_function_plot` function plots $H(j\\omega)$ and $-1/N(a)$ and prints out the amplitudes and frequencies corresponding to intersections of these curves. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<control.ctrlplot.ControlPlot at 0x11c4ca0d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Linear dynamics\n",
    "H_simple = ct.tf([8], [1, 2, 2, 1])\n",
    "omega = np.logspace(-3, 3, 500)\n",
    "\n",
    "# Nonlinearity\n",
    "F_saturation = ct.saturation_nonlinearity(1)\n",
    "amp = np.linspace(00, 5, 50)\n",
    "\n",
    "# Describing function plot (return value = amp, freq)\n",
    "ct.describing_function_plot(H_simple, F_saturation, amp, omega)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intersection occurs at amplitude 3.3 and frequency 1.4 rad/sec (= 0.2 Hz) and thus we predict a limit cycle with amplitude 3.3 and period of approximately 5 seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAGdCAYAAAAvwBgXAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjAsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvlHJYcgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAbyxJREFUeJztvXmYXVWV9/89d67x1jylKkllJJAQQiCQyIymQaVRFEH92fgq/ERF24bXt0X6Ebp/reG11dZXBbW1UV8HnEDtFhAUCCAECCYQQiYyVSU1D3eoW1V3Ouf3x7n73FtJDXc45+y9z12f56nnIVV32LU5dff3rPVdaymapmkgCIIgCILggIv3AgiCIAiCKF9IiBAEQRAEwQ0SIgRBEARBcIOECEEQBEEQ3CAhQhAEQRAEN0iIEARBEATBDRIiBEEQBEFwg4QIQRAEQRDc8PBewHyoqoq+vj7U1NRAURTeyyEIgiAIIg80TUM0GkVHRwdcrvljHkILkb6+PnR1dfFeBkEQBEEQRdDb24vOzs55HyO0EKmpqQGg/yK1tbWcV0MQBEEQRD5EIhF0dXUZ5/h8CC1EWDqmtraWhAhBEARBSEY+tgoyqxIEQRAEwQ0SIgRBEARBcIOECEEQBEEQ3CAhQhAEQRAEN0iIEARBEATBDRIiBEEQBEFwg4QIQRAEQRDcICFCEARBEAQ3SIgQBEEQBMENEiIEQRAEQXCDhAhBEARBENwgIUIQBEEQBDdIiBAEQRBEGdEfnsK3n3oT+/ojvJcCQPDpuwRBEARBmMtdD7+OJ/cP4d/+eAAXr2zCzRcvwyUrm/KalGsFFBEhCIIgHI+mafjj3gHc+L0X8NtdJ3kvhxvD0Ti2HxwGALgU4NlDI9j2yD6ua6KICEEQBOFoRifi+OyvX8OT+4cAAAcGorhqbRsCXjfnldnP71/tQ1rVcE5XHb75/g144C/HsGFxHbdoCEBChCAIgnA4X37sAJ7cPwSvW0HA68b4ZBKPvT6Ad21YxHtptvPwrhMAgPecuwhdDZX4wjVncl4RpWYIgiAcTV9oCsm0ynsZ3NA0DU8f1CMh931wI/7fi5cBAH764nGey+LCwcEoXj8Zgdet4J1nd/BejgEJEYIgCIfy/OERXPLlp/A3X38Gx0djvJfDhcPDMQxG4vB5XLh4ZRNuOL8LbpeCl4+N48BAlPfybOWhv+remMtXt6C+ysd5NVlIiBAEQTiU+546jJSq4chwDO++73m8cnyc95Js5/nDIwCA85bUI+B1o6U2gK1ntgIAflZmUZFH9vQDAK47V6yUFAkRgiAIB7KvP4Ln3hyBSwHOaKvBWCyBj/7oZUwn07yXZivPHdKFyFtWNBnf++AFSwDoEYJUmaStotNJ9IxNAgA2L2ta4NH2QkKEIAjCgfzguaMAgKvXteOhT2xBa60foclkWUVF0qqGHUdGAcwUIluWN6LS50Y0nsLRkfJIWR0amgAAtNT4Eaz0cl7NTEiIEARBOIyhyDR+t1v3A9x8UTcqfR7jIP7LmyM8l2Yrr58MIzKdQk3Ag3WLgsb3XS4Fa9prAQBvCNJd1GoODep+mFWtNZxXcjokRAiCIBzGgy/3IpnWsHFJPTYsrgcAvGV5RogcHuW5NFt5LiO6LlzWCLdrZp+MNe36gfxGX3kIkYODekRkZWs155WcDgkRgiAIh7Ezk37J7ZPBIiJ7ToQQnkpyWZfdMKPqRStO90Sc2a5HSMolInKQIiIEQRCEXbBhZmd11BrfawsGsKy5CqoGwzfhZDRNw54TYQDA+UsbTvv5mZm9eaMvAk3TbF0bDw5lIiKrKCJCEARBWMnIRBzD0TiUTLVMLiw983wZ+ERCk0lEplMAgO6mqtN+vrq1Bi4FGI0lMByN2708WwlPJTEQmQYArGihiAhBEARhISwasrSxCpW+mVM83rKiEUB5+ESOZhq4tdUGUOE7faZMhc+NZc16dGCvw9Mzbw7paZm22gCCFWJVzAAkRAiCIBwFM18yM2YuFy5rhKIAbw5NYDBzh+xUWCfZpU2Vcz7mzPZsesbJiGxUBUiIEAThQDRNwz/9dg/u+OWrZdfAi0VE1rTVnvazukqfcfj+1eH9RI6O6M27ljaenpZhMJ/IPodHRLL+EPHSMgBN3yUIwoH8ad8QfrKjBwAQmkzgOx/aCK+7PO679vXrYXjWJ+NUVrfWYG9fBEcc3sgrGxGZR4iUSS+RQ0OsYoYiIgRBEJajqhq+9sRB499/3j+EO375KlTV+ZUR8VQah4f1u98zO2YXIsua9YOZPc6pHMsIraWNc6dmmFg7OhLDZCJly7p4wEp3VwoaESEhQhCEo/jj3gHs64+g2u/Bv9+wHh6Xgt+/2oc/7x/ivTTLOTQ4gZSqIVjhRXswMOtjmEHzyLCzIyLHRjOpmXkiIs01fjTX+KFpwH6HTuINTyUxGNGrgla2UESEIAjCUlRVw7//SY+GfOQtS/HuDZ14/6bFAIBnDw3zXJotGP6Q9hooijLrY1hE5MjwhGP7Z4zHEkbTtiUNcwsRAFiREWY9GeHiNFiKqqXGj5qAeBUzAAkRgiAcxPOHR3FwcAI1AQ8+evEyANmS1RfKoGT1DUOIzJ6WAXTzpqIAkekURmMJu5ZmK8cWKN3NpbO+AgBwYtyZQqQ/rFdHddRVcF7J3JAQIQjCMezq0StBrjijxeiXcEG3XrJ6aGgCQ1Fnl6zuy0OIBLxuLMocSk5NzzAhsmQefwijs15/zInxKUvXxIuBjBCZK1UnAiRECIJwDHtO6i29cyet1lf5jFLWHUfGuKzLLthI+4XKNLM+EWcaVo9lSndn66h6Kiwi0uvQiEhfWBdYbSRECIIgrGc2IQIAm5c7Pz2TSKkYyrQqZ4frXCzLHNBOLeHNRkTyFyJOj4h0BCk1QxAEYSkjE3H0h6ehKMBZpwqRZboQcfKwt4HwNDQN8HlcaKzyzfvY5TmGVSfCKma65+mqyuhs0B/TF5pC2oEl3swjQhERgiAIi2HRkO6mKlT7Z/Zq3LSsAS5FT130h51553sypP9ei+oq5qyYYTi9hJf1EMknItJa44fHpSCZ1hzpISKPCEEQhE28fmL2tAwA1Aa8xvedmp7pywiRjrqFDxxWwtszNolkWrV0XXYTmswp3c3DrOpxu9Ce2TOnpWc0TTOESNlGRO6//36cffbZqK2tRW1tLTZv3oxHH33UyrckCKJMmcsfwrgwk57Z6dAZK4YQycML0FYbQKXPjZSqoWfMWSZNJiaaqn2nTR+ei846VjnjrL0YjSWQSKtQFKC1tkyFSGdnJ+69917s3LkTO3fuxBVXXIFrr70We/futfJtCYIoQ17PCJG1cwiRMzLTaA8POdMXwaoj8ukXoSiKUVHitPTMcMaw21KT/8FrGFbHnBURYdGQ5mq/0LOWLF3ZNddcg7e//e1YtWoVVq1ahS9+8Yuorq7Gjh07rHxbgiDKjJGJOPqYUXWuGStNGV+EQytFTob0Q2dRno2rnFrCOxjR96G11p/3c5zaS6RfAn8IYOP03XQ6jV/96leIxWLYvHnzrI+Jx+OIx+PGvyMRZ09EJAjCHHKNqnO1sWa+iOFoHNHppLDtrosl6xHJT4h0Z/wTxx2WmhkqJSISctZeDEjQQwSwway6Z88eVFdXw+/349Zbb8XDDz+MM888c9bHbtu2DcFg0Pjq6uqyenkEQTiAvQv4QwCgJuBFc41+l+y0dISmaQWZVQGgPSNYWPjeKRQXEXFmL5FsRETcHiKADUJk9erV2L17N3bs2IGPf/zjuOmmm/DGG2/M+tg777wT4XDY+Ort7bV6eQRBOAAmLBbsKJrxRRx2WDoiPJXEZCINIP+ICAvXMwHjFFhEpLkAc6ZTe4nIUDED2JCa8fl8WLFiBQDgvPPOw8svv4xvfOMb+O53v3vaY/1+P/z+/FUsQRAEkL2T7WqYv1xzWXM1Xjw65riICOsh0ljlQ8A7/5A3BrtLHog4KyIyxCIiNfmfJaf2EhE9gpAvzMAsukfEdhutpmkzfCAEQRClwuaEdC3Q2tzoKDrirIhIX6jwCavsLjk0mcRUJpriBAyPSAEREaf2Ehmg1Azw+c9/Hs8++yyOHTuGPXv24K677sLTTz+ND37wg1a+LUEQZUQipRp39az6YS6WO7SjaKH+EACoDXhQ5dOjJ07pNquqWk75bmHRddZLpNch5l1N06hqBgAGBwfxoQ99CP39/QgGgzj77LPx2GOP4W1ve5uVb0sQRBnRH56CpgEBrwtN1fPPWGGVM0dHYlBVDS7X/K3QZaHQihlA7yXSFgzg8HAMA+Fpo5xXZsYmE0hlPB7NhQoRhxlWQ5NJxFN619yWAoy7PLBUiPzgBz+w8uUJgiCMg6OzvnLBGSud9ZXwuV2Ip1ScDE0t6CmRhdw5M4XQHqzA4eGYcecsO6xiprHKV3ADL1ZF5JS9YL9HU7Uffk9+viFeiNtqjSAIIg9YKL1zAX8IALhdijF/xEmVM8VERIBsyN4pqZli/CEMlsphqR3Z6ZfEqAqQECEIQnKyEZF8O4o6r7V5MWZVIFeIOCMKMBwpzh+S+5xhh0zgZf9PRZ4xwyAhQhCE1LBBZQsZVRlGa3OHVM4k0yoGo0yIFHbotAWdlY4oppkZg0VRhhwSERmZYNEhsf0hAAkRgiAkx+ghkq8Qcdiwt8HINDQN8LoVNFUVduiwklWnCJFi2rszclMzqgOamo3FEgB0v4zokBAhCEJqesfz94gA2dTM8VFnlGmOTOgHTnO1v+AqIJaaGXCIR6SUiEhTtf6clKphfDJh6rp4MDpBQoQgCMJy4qk0BjO+gHyFCPNRDESmHdHOeyQTBWisLvzwba/V92LcIU3NjPbuRUREfB4X6iu9M15HZkZj+u/QUMR1YTckRAiCkBZm0qz0udGQ551fS00AbpeCdE7zK5lhB85CPVRmo7bCg8pMUzMntHofKiEiAmRTOo4QIpmISBNFRAiCIKzjRE5aZqEeIgy3SzHmkDihbJWlZoqJiLCmZoD8e6GqGoYnii/f1Z/nnBJe5hFpKEKg2g0JEYIgpKV3LNvMrBCc1LyKVUc0FRmC72CVMyG592J8MoFkOtNVtci9YN1YhyQv4U2rGsYmmUeEUjMEQRCWcaJAoyqDRQFYIzCZYRGRYlIzQHYvZE/NsHRKQ5UPPk9xR5uRmonIHREJTSagZexPzPciMiRECIKQlkJLdxkdDmrkxcyqxUZEnNJdlVXMFNPMjOGU7qqjmbRMfaUXngJb3fNA/BUSBEHMQbERkXajkZfchy+Qa1YtVog4IzVTSnt3BvOIyJ6aYUbVfA3cvCEhQhCEtAxkIhptBc7T6HBQI6+sWbW4Q8cpbd5HS0xRAc6pmmHiVAZ/CEBChCAISdG04qsknBIFSKVVo/lWsRERZtBkeykrbB8aKksRIpmISCQOTZO3x4zRVVWCihmAhAhBEJISnkoaVRKF3gWz1uZD0Wmk0qrpa7OLsYwpUVGKD8MzATMWS0jd2pwdvvUlpCOYKJtKphGTuMHbCKVmCIIgrIcZCoMVXvg97oKe21Tlh9etQNWAQYnD8CPRbBTAXWB7dwa7a05L3tp8PFb64Vvl96Aq0+BtSOIqorFY8d12eUBChCAIKRk22nkX/mHrcinGePR+iUt4SzWqAoDX7UJdpsST3UnLCOubUV9CagZwxhRemebMACRECIKQFOZpKLZ5FWvk1SexSZM1MyvVC8CEzIjEPhEzIiJAblMzefdilDwiBEEQ1jNslGsWWbZaJ//k2WylSGkheOaxkVmIjJkkRLKGVXkF6uhEtrmbDJAQIQhCSozUTIn9M/okrpwZLrG9O4M9X9ZGXsm0ish0CoAZQkQXqLLuBZAVZaVeF3ZBQoQgCCkpxSMC5PYSkTciwsyq5qVm5PSIhCaTAPTqoWBFaS3Ns03N5BQiekm3vh8UESEIgrAQwyNSpBDJdleVNyLCzKrFRoUYbA9lTc2wap+6Cm/R1UMM2du8j+eIslKNu3bh4b0AgiCsYXQijvuePoz2YACbuhtwVkew5A9pkSg1ItJuDL6TV4iYZVZtltysyrwypfQQYTRLLkSYOK0voaTbbkiIEIRD+bc/HsCDL/ca/75sdTN++D82cVyRuZSemtEjIiMTcSRSatETW3nCUjMle0Rq5DarmtFVlcHSGazyRDbGJCvdBSg1QxCOZHQijod2nQQAbF7WCJcCPH1gGIeHJzivzBySadU4KIpNS9RXeuHPiI9BCSskNE3L9hEpYeIskOMRiUp6+JrQVZXB5rOMT8rZaXbEpOohOyEhQhAO5Gcv9iCRUrG+M4if3XIBLl3VDAB4+K8nOa/MHFgo3u1Sis6DK4qSrRaRMBIQmUoZLe5Lvftl+zAak3PGitFDxISISH2VbnZNqxoi08mSX89uxkyqpLITEiIE4TASKRU/3nEcAPCRi7qhKAres7ETAPDwrpNS3uWdCkvLNFX74CohD26YNCX0A4xkoiE1fg8C3sJa3J8K85gk0xrCUxIeviw1Y0IDL7/HjRq/7lqQMT0zShERgiB489+v9WE4GkdrrR9Xr20HALx1TStqAh6cDE3hxaNjnFdYOsMTeiqlWH8IQ+aICBNPpaZlAP3wrQ3oh6+MPhEzIyJAVtCMSShEWAm2LF1VARIiBOE4fvPXEwCAD124xDBgBrxuvPPs9hk/l5lSm5kxmplJU0JvxIjJpsQmo1pEvr0Yy5SsmuERAXIMqxL2VTEG3lFEhCAIHqRVDa/2hgEAbz2zdcbPrjtXT888uqcfUxKPOAdy2rtnumAWS7MREZHPrMoOHLNC8DLPm8nOmSmtmRmDHeIyRkRCJosyOyAhQhAO4sjwBCbiKVT63FjZUjPjZ+ctqUdrrR+xRBqvnQjxWaBJlFq6y2iqkbdaxDhwTEpHyNxLxKiaMSs1YwgR+faCeXzqKkiIEATBgd29IQDA2kWnNy9TFAVnd9YBAF7vi9i8MnMptasqo1lijwjroFlnUhRA5sF3Zg28YzRUsSoieQVqXaU514UdkBAhCAfxaibScU5X3aw/X9sRBAC8fjJs04qswfSIiISHb2jS3CiArL1EphJpTCX1VKNZ6QipUzNT+ppLnbljJyRECMJBMH/I+kzk41TWddYCICHCMNIREpbvhqZYasakiIikoox1VfW6FaPstlQaJBUi08k0ppMqAIqIEATBgelkGvv69ZTL+q7grI9hEZHDwxOYTKRsW5vZmFU1ww7fWCIt3X6wAzhokhdAVrNqrj9EUcyZrcLKd2WrmmH+ELdLQbVJoswOSIgQhEPY1x9BStXQVO3DoswclVNpqQ2gucYPVYMhWmQjFk8hlqn6KTUiUuVzI+DVPwZlS0lkzapme0Tk2gdjzoyJVSKypmYMf0iF1zRRZgckRAjCIbyaMaqu76yb90No3SLmE5FTiLDDIeB1oarEuz5FUbLTViUr4TU8IiaX7w5PyNXm3eyKGWBmakamvWDXRFCitAxAQoQgHMOrJ3Tfx9lz+EMYazvk9omwg4cNJysV4wCWKCKiqlpOmaY5hw4TZImUimhcnjTVuAUtzdm1lUirmJBoL0ImXxN2QUKEIByCERGZwx/CWJuJiOyRVYhk7vrMMuPJWMIbmU6CjQyqMykSEPC6UeXTZ9aMS5SSyHZVNe/wrfC5UZGZ3yNTeiZslO7K00MEsFiIbNu2Deeffz5qamrQ0tKCd73rXThw4ICVb0kQZclUIo0jIzEAeUREMkLk0NAEppPydVg1+w64ScLBd6yHSJXPbbTxN4N6Cb0RZs+ZYRht3iXaC1a6SxGRHLZv345PfvKT2LFjB5544gmkUils3boVsVjMyrcliLLj2Kj+N1VX6V3wgG4PBtBY5UNa1XBgIGrH8kzFbE+AjIPvQkZUyJrDlxlAZWDMor1gQ+PGJDLvMrOqbB4RS+t7HnvssRn/fuCBB9DS0oJXXnkFl1xyiZVvTRBlxfGMEFnaWLXgYxVFwVmLgnjm4DD29kWwfo7mZ6JidpVEs4QREau6ZzJxNxZLmvq6VhK2IDUDyNlLJCRhe3fAZo9IOKznpBsaGmb9eTweRyQSmfFFEMTCHB2ZBAAsbazM6/HLm3XBwgSMTLBD0rwZK/rryBQRGTe5qyqDlQLL5BGxqpOojKmZsITt3QEbhYimabj99ttx0UUXYe3atbM+Ztu2bQgGg8ZXV1eXXcsjCKlhgmJJHhERAFjSoAuWYxIKEbMnrTZL2FHUsogIiwJIlJph1UNmC5FGCQffjZts5LYL24TIbbfdhtdeew0///nP53zMnXfeiXA4bHz19vbatTyCkJqjGaNqd1OeQqSRRUQmLVuTVYxZ1T8jKk//jJBFBw4zfMoUEWFRALM6zDJkHHxneEQkM6va0gP2U5/6FH7/+9/jmWeeQWdn55yP8/v98PvN6Q1AEOUEExRL8kzNsMf1jE1C0zSpujCaXSXBhMh0UkUskZaiNfb4pLnpKYZsVTNpVTN6nlgXEZFjL4BsdIjKd3PQNA233XYbHnroITz55JPo7u628u0IoiyZSqQxENG7guYbEemsr4RLASYTaam8EUCOP8KkiEiV34PKTP8MWQyrIYsOHNmqZqLTSbAgllUeEZmEiBEpkywiYqkQ+eQnP4mf/OQn+NnPfoaamhoMDAxgYGAAU1NTVr4tQZQVx8f0tEywwpv3weTzuNAe1OfR9EiUnlFVzYgGmNlJU7YSXqsOnGzVjByHL4sAVHjN7acCyDf4LpFSjRlM5BHJ4f7770c4HMZll12G9vZ24+sXv/iFlW9LEGXFMVYxk2c0hLG0iRlW5REi0ekU0pmWomZ+2MpWwpuNClkTBWBiT3SyqQjzD17ZUjNsLxQFqAnIJUQsTYbKYvwiCJk5ZvQQyc8fwljcUIW/YBQ9ElXOMKNqtd8Dv8dt2uuyQ0eWypmQRa28mbAJTSaQVjW4XWJ7h6yqmAGyomwqmcZUIo0Kn3nXmxWEM2XMtQGv8P/fToVmzRCE5BRaustghlWZIiJWRQKMLpqSNPIKWWVWzbyeqgGRKfH3ggmRWguESLXfA69bP9Bl8MxYVdJtByRECEJysqW7hUVEWATl+JhEQsSCke+5ryfDgZNIZSfCmu0R8bpdqAnogXIZ9sLKclVFUYySYJn2QjajKkBChCCkJ1u6W1hEZHGDfN1VzZ4zw5CpQoJ1ElUUayIBMomysMVj71mn2ZAEnhlWSRWUrHQXICFCEFIzlUijP5wp3S0yNROaTBof6KJj9pwZhkxlq+GcKIAVXoBsLxHxr4mIhR4RICvKpBAikpbuAiRECEJqejJpldqAp+DccJXfY5StylLCa/acGQY7fGUo1Ry3OATfING8GSvNqkB2iq0UAtXCCiKrISFCEBLDhMiSxqqiuqNmDatypGfMnjPDaJAoHTFu0dh7hkzzZqwee59NzcizFxQRIQjCVvrDenPA9mCgqOfntnqXAbPnzDByPSKitx0wxt5bdPjKNG/G6oiIVKkZ8ogQBMGDvpDuD+moqyjq+UsyhtVjI5JFRCwyq8ZTKiYz3SlFxShhtjoiQkIkJzUjgRAhjwhBEDwYKDEi0tWgC5i+sBxjF6yKiFT6si3CRT+Axy1OR0hl3LUpIsKahYkMeUQIguBCX6Zipr3IiEhbRsCwyhvRyXpEzBUiiqJI4xNhh6JlERGJ5s1YLURYdEGOiAgJEYIgOFCqR4QNvhsITwvvjUirmpEHt+IQlqWXiNUHjizzZlLpnMZuFomyOknEKZBNzbAmbDJBQoQgJEVVNQywiEiRQqStVn/eZCKNyHTKtLVZQXgqO/LdikNYFiESmbY2CsAqksTfh+z1WhuwZmwaGyUQFlyUqaqGaEaU1VZYOkLOEkiIEISkjMYSSKY1KArQWlucEKnwuY1DfUDw9Aw7GGsDHnjd5n90yWLSNOarWDRhNeuLSCKVVi15DzNg+1Dt98BjwfUAAHWZ6EJoKil0xHAikTJEulXXhZWQECEISWFpmZYaf0kHM4uK9AtuWLWqqyqjQZLmVZEpa+98cyMtIYE77mZTEdYdvEykp3MiDiLCOsz6PS4EvGJPCZ4NEiIEISmsdLctWJxRlcHSOrJERMyumGE0VPkz7yPu4QtYn5rxuF3Ga4vcyMtqoyoABLxuVGQO9pDA10VWnMoXDQFIiBCEtLAIRkeR/hAGEzKiV85Y3Sch642IW/L6ZqCqmnH3a2UIvkGCeTN2CBEgGxUROVLGxGmNRV4ZqyEhQhCSkjWqlhYR6ZAkIpLtk2BtI69xgQ/fWCIFlXkBLDyAWddWkf0yVg+8Y7DrTeQ0lR3i1EpIiBCEpPSVWDHDMHqJRMQWIqFJi6tFWP8Mge98mRjzWewFqJegbNXq64FRJ0GailUQUWqGIAhb6Q9leojUlSZEsr1ExDarWh2Kb6gWf8aK4QWw+M6XdW0NCxwFsKuTKCvhFfm6iE6ziAilZgiCsJF+k1IzsnRXDVl88OR2VlVVMUs1s0ZVaw8co2xV4P4ZRhkzpWbIrEoQhP2kVQ2DETbwzpzUTHQ6ZXSqFJGwxaF4duComriRAPsOXxYRETcKYJtZ1UjNiHlNAFmBSh4RgiBsY2QijpSqwaUAzdX+kl6r2u8x3PYiG1atDsX7PC5jH0T1idhlSmR7LPLhG7JJiDC/jNAeEUOgUmqGIAib6Mv4Q1prA6Z0lZShl0hoyvpZGsacFUH9AMyUaPXhG5QhCmCTRyRbvivwXlBEhCAIu+k3qWKGke0lIq5h1erUDJC9+x0VVIiEbbrzlcEXYV8fERkiIrpApT4iBEHYRp9RMVOaUZXRXit2RCStakY0wMo7YOEjInalZirYsDcx9wGwfuYOg/VUEVmUGRERMqsSBGEXzKjaVuSwu1MRvZcIK08ErL0DNjqKCnoAW93enVEn+OGbTKuYTKQB2NhZVVBxClBqhiAIDgxF9TbkrbWlGVUZontEmFehyue2ZPIuQ5qIiOWVIvo+TCbSiKfSlr5XMUxMZ6u7rE5HsNRMZDqFtKBl3VHDO0SpGYIgbGI4I0RaasyNiLCUj2jYXSEhqkfEroZmNQEPFEX/bxFLmVkEoMrnNsWsPR+5s41E3AtNs2f+kJWQECEICWERkeYasyIime6qgqZmDGOiRXNmGPWCl63alZpxuRTjPcIC7oWdDbw8bhdq/HqkQcSW97FE2pb5Q1ZCQoQgJCQbETFHiLAUT2gyKWQo3urJuwzRKyTsqpoBchp5CRgFsNsTUVclrkBl0RCf2wW/R84jXc5VE0QZM51MGweSWRGRYIUXXrceix+dEO8Qtm/SqriHL2DvlNVgpbht3u1u4CVyU7NsxYwHCsunSQYJEYKQjJEJPRric7tMO5gVRUFTpkMri7aIBDsM7WpeJeLhm0yriNlUKQKIPXXW7oiIyA3esj1E5EzLACRECEI6cv0hZt4BsegKEzoiYVfzqtw7X9EG30VtrBQBcufNiHz42hMRMfwyQu6F3JN3ARIiBCEdwyYbVRnNIkdEDLOqPa3NVQ2YSIg1AJAdONV+j+WVIoDYw97sbuAltBCRvJkZQEKEIKTD7IoZBns9IYWIDe3dASDgdSPg1T8WQzGxDp2wzXe+hkdEwAm8LDpkd2pGRCFi915YAQkRgpAMsytmGIYQETA1Yww4s3DgHaNe0APY7jtfoSMiNptVRRYisk/eBUiIEIR0DEf1Xh9lFRHJiAKrzaqAuMZEO3tnAIJ7RDiZVWkvrIGECEFIhtldVRkiV83YZVYFshER0ZpX2TXkjSFyBRGJsix274UVkBAhCMmw3CMiYGrGLo8IIO6hk9svwg6CFWKmqAD7owC1UkREKDUzK8888wyuueYadHR0QFEU/Pa3v7Xy7QiiLLDMIyJoRGQ6mUY8pQKwvmoGEDcSYFdTN4ao+wCQRyQXJkSoj8gcxGIxrF+/Ht/61resfBuCKBtUVbOufDfzepOJNGJxcUpX2Ye/26UYMz+spI5SMwCyZtXodAqptGrLe+ZLhKpmDLKpGXkjIpau/Oqrr8bVV19t5VsQRFkRmkoilWm0xTwdZlHl96DS58ZkIo2RiTiqbDj08yG3bNWOFtbsABZt2Jtx+NrcO4O9d0OV9RVL+ZBWNUzE+TQ0S6RUTCfTCHjdtrxvPkTJrGou8XgckUhkxhdBEFmGMhUz9ZVe+CwYcCVi5Uy2vbs9B6Go82bsTs3kTp0Vqc37xIwOs/bsRbXfA7dLF8GiparsFqhWIJQQ2bZtG4LBoPHV1dXFe0kEIRRWVcwwRPSJsEPQvgoJ0VMz9kWqggKKMuaJqPC6LRHjs6EoirHvIqVnNE2zdRCiVQglRO68806Ew2Hjq7e3l/eSiDJgMpHCaydC2HMijMPDE9A0sWaM5DIUscYfwjBKeAWqnAkbzczs9UaIl5qxv5W3UUEk0F6EOTXwYgJVJCEylUwbqVryiJiE3++H32/NByxBzMZ0Mo3r7nse+weixvfuevsa3HLJMo6rmhsmEKwSIiKmZgwhYkPFjP4+YkZE7E7NANlOtiKV8PJq4CViCS8zqnpcCioE8q0UilAREYKwm3sf3Y/9A1H4PS6jHPYrjx/A0ZEY55XNDouImF26yxBZiNh1ANfn9BERZQKvHoK33wsQFLCEl1cDLxErZ3KjZHYYua3CUiEyMTGB3bt3Y/fu3QCAo0ePYvfu3ejp6bHybQkiL7YfHMYPnz8GAPjO/7MRL37+Sly0ognxlIo7H3pNyBSNXRGREYFSM4ZZ1aaDhx1wqgZEBSljjqdUJDIltPZGRAQUIpwaeAkpRKZYDxGhkhsFY6kQ2blzJzZs2IANGzYAAG6//XZs2LABX/jCF6x8W4JYkMlECp/91asAgL/bvASXn9ECRVHwpXevQ8Drwo4jY/jlTvE8SkMRa+bMMEQ0q2Y9AfYcwAGv2whzi1ItwvbApQBVPvtC8CJ2mY3YfD0wghXimVWdMGcGsFiIXHbZZdA07bSvH/7wh1a+LUEsyCN7BjAUjaOzvgJ3Xr3G+P7ixkrc/rZVAIDvbj8iXFSkHD0iIcMjYl8fi3rBUhK5h6+dIfjsAEAxBBmQLVe1OwpgREQE2ovotPzNzADyiBBlCot2vH/TYlSccof5gQuWwOd24chIDG8OTfBY3pwMRywu382ZNyOKCGMf/HamJIKVzKQpiBCZtt+omvt+kWkxUlQAuJWripyaoYgIQUjG0ZEYXjo6BpcCXHfuotN+Xu334KKVTQCAx14fsHt5czKVSBueBasiIo3V+gGcTGvCfODaXTUD5EZExLj7tbu9O0PEwzfKqYEXqyASaS/sbnVvFSREiLLj16/o0ZBLVjWjPVgx62OuOqsNAPDYXnGECEuX+D0uy4x6fo/bOHyGBEnPhGzuIwKIN/CN1zwRIUtWqXzXwO7hf1ZBQoQoK9Kqhl+/cgIA8L7z5u7c+9YzW+FSgL19EfSOTdq1vHkZnsgaVa30CTRloiKjE/yjAaqqcemfEWT9M0QRIpxTM3T4CroXZFYlCPl47s0RDEbiqK/04so1LXM+rqHKh03dDQCAPwoSFbG6hwijsUp//dEY/4hINJ4Ca+VhZyiepWZEaWrGOpvaHgXIvF9EqMOXTzoiK0RE8svwMe6aDQkRoqz40xuDAIB3nN0Ov2f+MkiWnhFFiFhdMcNgPpGxGP9DmB2AAa/L1omnopWt8mjvDmQbmsUzU2dFgFv5bmVWlIli5OZ1XZgNCRGibNA0DU8fHAIAXL567mgIY2tGiOw8Pi7EgTRkccUMg417FyE1k21mZu8IeqO1uSAREXbna3dqptrnQWborDBREd4NzRJpFVOiiTJKzRCEHBwZiaF3bAo+twublzcu+PiOugosbqiEpgGvnQhZv8AFYGZVyyMiTIgIkJqxu707o85IzYhx+PKYvAsALpcilElTVTVMxPlUzVT53HBnVJkIewHwqyAyGxIiRNnw9IFhAMCm7gZU+vL7QN+wuA4AsKsnZNGq8oelZqz2iLCIiAipGTZsLWhj6S4g3qRVniF4wycyzX8vovEUWFbEbl+EoijZyczCXRfkESEIKXj6gJ6WuWx1c97P2dBVBwDY1TNuxZIKYihqbXt3RmOmzbtIqRl+ERH+ewDY3+Y+F5GqRaKZg9fvcS3o8bKCbHdV/nsxYxAipWYIQnymEmm8eHQMQIFCZHE9AGB3b4i7QY2lZqz2iGRTM/wP4TCHHiK57xcRZAIvzzJNkYRItkqEz8ErUpoqdxAipWYIQgJeODKCRErForoKLG+uzvt5a9pr4fO4MD6ZxPFRfv1E0qqGkUyEwuqISINAVTM8uqoCMyfwTiT4l2vyMqvmvqcIUYBsPxU+qQixRBmfQYhWQEKEKAu2Z/whl65uLqgZmM/jwtqOWgDArl5+6ZnxyQTSqgZFyZbXWgXrI8LekydhTqmZgNeNgNc1Yw28UFWNqxeAvacI82Z4le4yhBIimWuiJmDvIEQrICFClAU7juhpmYtXNBX8XCM9w9Gwykp3Gyp98Lqt/bNlzbw0jb9HImtWtbd8FxDn0JlIZA2aPFIzIqUjeM9WCeak7HgT5tT23wpIiBCOJzSZwIHBKADg/Ey31EIwKmd6QyauqjDsamYGAB63y0iF8E7P8CrfBXJ7ifA9dNih5/fY29SNIYogA8SJiIgwldkp7d0BEiJEGbDzmJ5SWdZchabqwg9yFhF5oy/CrbvkUMSeihlGoyBNzbINzcrXpMmzYgYQZx9y12B3PxWGSBGRqEMm7wIkRIgy4KVjelrmgiKiIQDQEQygucaPlKrh9ZNhM5eWN9keItZWzDBEmTfDMyLCepew9BAvsiWafA5fkebN8G5pbggRofwylJohCOF5KVO2e/7S4oSIoihYtygIANg3EDVtXYXAPCJ2RUREaWrGq2oGECcSwGvyLkOUfQD4Vg8B2UNfiL2g1AxByMFkImVEMYoVIgCwuq0GAHBgIGLKugrFrq6qDFbCyzM1k0ipmEzoqTC7Z83o7ylG2aooqRmhIiK8+oiIFB2ackZ7d4CECOFwdvWEkFI1dAQD6KyvKPp1VrfqQuTgwIRZSyuIYZsjIk0CzJthB7Ci8BlzLkokgPdgM1H2AeCfjqg1UjMC7AVFRAhCDlg31fO7G0qqtV+VESIHBqNcOqzaHhERIDUTzngzagNeuFz290lg6SDuVTPTvNMR+vvGEmmkMp08eSFK+a5IooyHSDcb+X8DwnZUVcPBoSheOT6OwUgcF69swsbF9VwOi4V4OSNENhVpVGUsa66C26UgPJXEUDSO1lp7TKMMu6tmGgSYN8PTqAqI0z+DexQg56CLTKcMkcoD3uW77H2nkyriqTSXeTeMiEMm7wIkRIgCeaMvgs/8YhcODmZTFP/nz4fQWuvH59++Btees4jj6maSSKlGN9RNJfhDAL3T5tLGShwejmH/QNRWIRKLpxDLeCVabHrfJgHmzRiluxyMqvr7ZvqIiCJEOEUBPG4Xqv0eTMRTCE8l+QoRIx3B5+iq8XugKHqzv+h0Cv5qfkIkynkvzIRSM0ReaJqGH79wDO+67y84ODiBSp8bb1nRiGvWd6Am4MFgJI6/f3A3vv/sEd5LNdhzMozppIqGKh9WtOQ/X2YuzmjTW70ftLlyhg27q/C6bZspIcK8Gd4REVFMmrz3Ife9eUaHVFXDRJxvFMDlUlDtF6Nyhnd0yEzkl1KELfzHs0fwpUf2AwCuPKMF/3b9euPOKJ5K48uPHcAPnjuKf/3DPsTiafz9W1fyXC4A4OVM/5DzltSbMothVWsN/rCn3+jSaheGP6TWb9tMCfb/ls2bcXNIu4U4zZlhGF00Obe55907A8j6EHiKsmg82+qepy8iWOFFdDrFXaDy9suYCUVEiAX5/at9hgi5422r8P2bzpsRnvV73Pind6zBZ/9mNQDg3/90EC8cHuWy1lxeMskfwljdpkdVDtosRIweIkV0hS2Whkxague8mRDHHiJAtnw3lkgjydGkybt3Ru5784wCsIM/4HVx9WYYJbycm5rx9g6ZCQkRYl52HhvD//zlqwCAj7ylG5+6cuWsd+WKouCTl6/ABy5YDAD47K9fRSzO7w9VVTXsPGauEGGVMwcHo7ZOpR2O6kbVllr7hIgI82YigphVc9fCgzBnjwggiBARpFxVhKZm08k04ik1sx6KiBAOJjyVxN8/uBuJtIqr17bhn96xZsHnfP7ta7CorgInxqew7dF9Nqxydg4MRhGZTqHK58aZ7bWmvOaSxir4PS5MJ1X0jk2a8pr5MBS1PyICZNMzvCpnWEqERzMzAHC7FCMFwNOwmk3N8E1HALwjImJUiYjgHWJzZhQFqPZRRIRwMHf/7nWcDE1hSWMl/u369XmV51b7Pfi3954NAPjJjh68ymliLUvLnLukHh63OZe526VgZauenrHTJ8LMqnZVzDCaOM+bIZMmkExnu8vy3AcRGnnxrphhsIiMCNGhar9HyLYJhUJChJiV3+0+id/u7oPbpeDfbzjHcIrnw5YVTbhug17G+/U/HbRqifPCBt2VWrZ7KkZjMxsrZ3hHRHilZlgUIsjJIwJk/Sm82rzn3nUX8jdoNiJEAUSpEhFClAmQrjMTEiLEaYxOxHH37/cCAG67fAXOXVxf8Gt8+sqVcLsUPHVgGLt6xs1e4rxompYddGeSP4SxskUXIoeH7Wv1ziIizTZ6RAD+82YoIpI1RFb7PaZF9oqB9z4A4lSJZEUZPw9c1EHNzAAq37WFZFrFsZEYDgxGMRSJw+91ocrnwdmdQXQ3VdlWkpkv//qHfQhNJrGmvRa3XbGiqNdY2lSFd29YhF+/cgJf/9Mh/Ogjm0xe5dwcH53EcDQOn9uFc7rqTH3tZc1VAIAjwzFTX3c+uEVEKrMlvDwIc25oBmT9KbxKeHkbdhlCCBFBqkRqBShlFiVNZRbO+C0ERNM0/OXNUfz+1ZN47PWBOUu9Wmv9eMe6Dtx8cTc66oofymYWzxwcxsO7TkJRgHuvWwdvCXdhn7piBR7edRLbDw7jrz3jRUVWioFFQ87uDCLgNbfMb1mTLkSOjsSgaZrlIjKtahiLZfuI2AnP1IymadnUjADeiDCnu1928POeJ8IOf55RABGqhwBRUjMUESHmIa1q+MOeftz31JvYn+MjqPK5sbK1BovqK5BMqRiLJfDaiTAGI3H851+O4scvHMN7N3bic1efYbSWtpupRBp3/XYPAODDW5ZifYnRhCWNVbhuwyL86pUT+MFzR3HuB2wSIiaX7eayuLESLgWYiKcwHI1bbiAdnYhD1QCXAjRW8REiPCIisUTaKJHmVTUD5Ay+m+IUERGgmRkgSEREsL0QIyJCQoQ4hZeOjuGe3+/FG/0RALr4uHbDIvzt+g6cv7ThtO6U08k0nj88gu8/exTPHx7Fgy/34sn9Q/jSu9fhrWe22r7+r//5IHrHptARDOCOratNec2PXNSNX71yAo+9PoCB8DTagtZXfrCOqmb7QwC9eVtnfSV6xiZxeDhmuRBhaZnGar/t3U3rjYiI/R+4LBXi87gQ8JavN0KEZma57y9C+S7vvRBhGKIoaSqzILOqCfSFpvCpn+/C+777At7oj6Am4ME/vHUVnv/clfjSu9fhwmWNsx4iAa8bV5zRip/dciF+fetmLG+uwlA0jpt/vBNfemSfrU2z9vaF8f1njwIA/uXataY59Ne012JTdwPSqoafvXjclNecj8HINI6PTsKlABuXWBOBYT6RoyPW+0SGOflDgKxHZIxD+W6uUZWnh4p1V+VVNSNiOkK18XMpF1GiACJ0VhVlL8yChEgJTCfT+OafD+HKr27Hf73aB0UB3r9pMZ7+n5fh79+6sqCyw/OWNuAPn74YN1/UDQD43jNHcMuPdxoTFq0krWq486E9SKsa3rGu3fRozE2blwIAfvZSD+KptKmvfSrMH7KmvdayP9JlTXovkSM2VM5ke4jYL0Tqq/T9G48loWn2Hj6GUbXMIwEiNDMDsgeepgETCT4HsChRgNzUjN1/FwwWHeLtHTILEiJFoGka/uvVPlz51e346hMHMZVM4/yl9fiv2y7CtuvWobHIu9eA141/eueZ+MaN58DvceHJ/UP4wH+8aLlZ8AfPHcFrJ8KoCXhw9zVnmv76W89qRVttACMTCTy6Z8D018/FKNs1uX9ILt02RkSGMu3deUREmCclkVYRS1grIE9FhNJdINvDhFdnVVH2IeB1w+/Rjwte0aGoIOW7TAilVM1oNmc3ovhlzIKESIG8diKE67/zAj718104GdL9FN+48Rz88mObsXZR0JT3uPacRfjlxzajscqHPSfDuPF7L2AoMm3Ka5/Km0NRfOVxvenYP71jjSWeB6/bhQ9mZtD83x3WpmeYP+QCC/whjOWZypkjdqZmauwXIhU+t+HPGLe5cob3wDsG94iIIKkZQKC94Hz4Vnjd8GRS7bwqZ0QRZWZhixC577770N3djUAggI0bN+LZZ5+1421N5bUTIXzip6/gb7/1F+w8Po4Krxu3v20V/nzHZbj2nEWm57HXd9XhFx/bjNZaPw4OTuB9330BJ8bNnW+SSqu441evIZFScemqZrzvvC5TXz+XG87vgtul4JXj45ZNrw1NJozW6+dZGBFZ1qynZnrGJpFIWTuVlZlVWzgIESDXJ2KzEJkU49BhFWzhST5heOZD4B0RyV0Dj2qRtKohGmeHL990hKIo3JuaiZKmMgvLhcgvfvELfOYzn8Fdd92FXbt24eKLL8bVV1+Nnp4eq9+6ZMJTSTz4Ug/e950X8Lff+gseyaQVrtuwCE/+z0vx6StXosJn3TjqFS3V+NXHtqCroQLHRifxvu+8YGo64L6nD+PV3hBqAh7c+551lpoCW2oDuPKMFgDAgy/1WvIeO4+NQ9N0M6mVEYTWWj8qfW6kVQ29JovDU8lGROydM8Oo59RLhN118yzdBbKHbyKtYjppreicjbAgUYDcNfCIAkzkGENrBIgC8K6cIbNqgXzta1/DRz/6Udx8881Ys2YNvv71r6Orqwv333+/1W89J5qmIZFSMZ1MYzKRwlgsgeOjMbxyfAy/fuUEtj26D+/69l9w7v/3BD730B68dGwMbpeCd29YhMc+czG+dsM5aA/a03xscWMlfvmxzVjWXIW+8DSu/84Lpsw5efbQMP49MwfmnmvOsuX3ef8mPT3z0K4TmE6an1t94cgoAGvTMoB+R9TN0jMWd1gd4mhWBfg1NQtn+nbwTs1U+dxGxRuPXiJRIzXD/86XZ2qGHbwVXjd8Hv6OAt7dVUUpZTYLS6/uRCKBV155BZ/73OdmfH/r1q14/vnnT3t8PB5HPJ4tFYxEIpasa/vBYXz4gZfzeuyq1mq8e0Mn3rWhwzbxcSrtwQr88mOb8aEfvIR9/RHc8L0X8OOPbMLZnXVFvd7J0BQ+/fNd0DTghvO68J6NneYueA4uWdWMjmAAfeFp/HHvAK49Z5Gpr//coREAwFtWNJn6urOxrLkae/siODoyAcCani+apnEt3wX4NTUTxaSpKArqKrwYjSUQnkra/hnADmCeg/8YPIVIWLBUBM/oUCKlYipzI0cRkTwYGRlBOp1Ga+vMD+rW1lYMDJxePbFt2zYEg0Hjq6vLGs+Ca5YURKXPjUV1FdiyvBEfuGAxvnL9ejz3j5fj8X+4FB+/bDk3EcJoqvbjwVsuxDlddQhNJvGB/3gRzx4aLvh1QpMJ3PyjnRifTGLtolr887VnWbDa2XG7FFyf8aH8/CVzU3NDkWkcGIxCUYC3LLdeiNgREYkl0sYHDg+zKgDUc/aI8I6IANkDOGRztYimacL0EQHEiIiIsA8A39RMbkuHagEiZWZgy29xqvdgrhkdd955J26//Xbj35FIxBIxsnl5I169eyvcLgUuBfC5XVwnW+ZLsNKLn9x8AW7+0cvYcWQMH37gZfzTO9bgw1uW5uXvCE0m8MHvv4h9/RE0Vftw/wc3mj6LZSHed34XvvnkIew4MoajIzHjQC+V597UoyFrO4KGr8FKltsw/I5VSlX53KjiNAKed0REBG8Ei0bYfehMJ1Uk07pBVoR9yKYj7DdoijZbhadZNXcis93dlq3C0tO3qakJbrf7tOjH0NDQaVESAPD7/aitrZ3xZQVetwvBCi+q/R5U+viO1y6Uar8HP/rIJrzn3E6kVQ3//F9v4Laf7TL6TczFocEobvzeDuzt00XIz2+5EF0NlTatOsuiugpcuqoZAPDgy+ZFRVha5qKV1kdDgGxE5OiodUIk28yMj1EVyJpVRyc4RUQEOHh4RQJYFMDtUlBloSk+X3hGAUSbNpvtrsovIiLKXpiBpSewz+fDxo0b8cQTT8z4/hNPPIEtW7ZY+daOxu9x4yvXn4273r4GbpeCP+zpx5Vf3Y7vbD98miAZiyXw7afexDv+z3PYPxBFU7UPP7vlQqxsreG0euDGjGn1N6+cMKX8VdM0IyJysQ3+EABYmhEiw9E4JuLW3BUNcfaHANnyXbsjIhFBPCIAvzbv4RyjKs829wyuqRmBImRA1qvCZy/Eig6ZgeWS6vbbb8eHPvQhnHfeedi8eTO+973voaenB7feeqvVb+1oFEXBLZcsw+bljfj8w3vw2okw7n10P7782H6c3VmH2govYvEUdvWMg42GuHx1M7Zdd7Ytg+fm44ozWtBc48dwNI4/7xvE1evaS3q9g4MTGIrGEfC6sHGpPRN+awNeNFb5MBpL4NhIzLRmdrkMhHVR2crx/xePqplkWjV6RvCaRJ0Lt4iIYIcvX4+IWA28ePZUEc0vYwaWC5EbbrgBo6Oj+Jd/+Rf09/dj7dq1eOSRR7BkyRKr37osWLsoiIc/8Rb8amcvfrGzF7t6QtjdG5rxmDXttbj5om5cd675jdeKwet24fqNnbjv6cP4+cu9JQsRZtrd1N0Iv8e+EPbSpipdiIxaJEQyHpF2AYTIuI3RgNwPdxHCz8GMGLK7fNeomBFEiPCsFBGtgRcTAXyjQ2LshRnY8pt84hOfwCc+8Qk73qoscbsU3LhpMW7ctBjHRmLY1x/BZCINDXpPDR5ekIW48fzFuO/pw3j20DB6xyZLWuP2g7oQsSstw1jaWIVXjo/jmEWt3pkQaeXqEWEVIwmkVc0Wcxz7cK/xi+HfykYC7DUmilQxA3COAgi2F1lRxsOsKtZemIFzJBUBQL9LX2pSJYqVLG6sxEUrmvDcmyP45c5e3LF1dVGvE5pM4IXDeiOzK9e0mLnEBelu0sXT0RFruqsOZlIzbTyFSCYaoGr6YWBHRRKbMyNC7wwg6xEJ2e6TYV4AMT6mc1Mzc1U+WoVoQ974ijLneUT4324QZcuNm/TS7F/u7EUqXZxp9Yk3BpFSNZzRVmPMgLELJviOWVQ508+ESJCfWdXrdhmjxkdt8omI0syMwevQEXUfkmnN6G9jF8bhK0gUgGdnVSbKagRIW5oFCRGCG287sxUNVT4MRuJ4+kDhzdkA4JE9/QCAt5foMymGpY0ZIWJBakZVNaMCqo1zM71Gm3uJhAVqZgZk1xHiZVYV5PCtzGl3b3f/DFH9MtF4CmnV3mGIol0XZkBChOCG3+PGe87V27wX01MkPJU0ynbfvq7N1LXlA4uIjMYSphv4xiYTSKY1KAq/ybsMuwffiRoJ4NVHRJQQfO7UWX4VRGJEAXJFwITNPpHotFgpOzMgIUJwhfUUeXL/kFGumi9/3jeIZFrDqtZqrGixvy9Ktd9jtF43OyrC9qKxyg8vZ8Om0UvEJiHCmpkFOU/eZeR2VlVtvPsVqbssg58oEys14/O4UJHpSs1NoAqyF2ZAQoTgyvLmamzqboCqAT978XhBz2VpmavX2p+WYXRn0jNHLRIiPEt3GUZExKbUDCuTFS0iomkw+pvYQdYXIc6dL4/uqqm0ajQNFEmUsYiE3eXMZFYlCAv4H1uWAgAeeP5Y3h9wQ5FpPHOQpWX4CZGlmcqZYyZXzohQusswmprZ1OadXQOieET8Hnf27tfOfiqC+SIAPibN3M7FIhk0eZmYKSJCEBbwN2e1YXVrDaLTKfznc0fzes4Dzx9DIq1i45J6rG7j167eqsqZAQEqZhgNNkdEwgLNmWHwSElQakaHRQAqfW7uacpceDU1E80vYwbi/F8lyhaXS8Gnr1wJAPjPvxxd8A97Ip7CT3boaZyPXbLM8vXNh2WpGaOrKt+KGcB+j4hoZlUguxY7u6uKWB3BRYgIGgHg0Wk2lVYRS+il06LtRymQECGE4Oq1bVjVWp1XVOTBl3oQnU5hWXMV3rrm9CnOdmJVRGRQoNRM1iNizweuaA3NgJmGVTtQVc3wo4goyOyNiIgZAcimZuzzDUVzKnSqBUpTlQoJEUIIXC4Ff3/lKgDA/U8fxr7+yKyPS6ZVQ6jccvEyuGxoOT4frJdIaDJpaufNAQG6qjIaMm3eKSKSreixmmg8BS1ToCOSL4JHFEDYiEjA/gm8bC9ES1OVinN+E0J63r6uDW9d04JEWsWnf74L07N0b9z2yH70hafRVO3Huzcs4rDKmVT43IZYMDM9I5JHhLV5t6OPiKZpOQ3NxCjfBbJ+FbsOHRYF8HtcCHjtG+S4EDwMmqJWifAQZVHBypjNgoQIIQyKouB/v+dsNFX7cWhoAvf8fu+MroW/2tmL//yLHg3513edJcwHtFE5Y1J6JhZPGWF53l1VAb2XCaB7c+Ipa1t7TydVJDLt/kWMiNh1AItYMQPw9oiIExkCeIkyMdNUpUJChBCKxmo/vvq+9QCAB1/uxbu+/Rf84bV+/O/H9uOuh18HAHz6ypW4imPvkFPpbmKGVXNKeJlRtdrvQbWf/wdOTcBjtPa2OjXBzKAel4IqnxhCE8hp825TakbEihmAt0dErL3gUTUjapqqVEiIEMJx6apmfOX69agJeLDnZBif/Nlfcf/Th5FIq9h6Zis+k6mwEQWzZ86wtExrLf+0DKD7d+ozB7HV6ZlsV1WvrdNdF8LuA1jEZmZA9gC006ApWldVRrahGYcmd4KJslIR6yoniAzv3diJS1Y14d5H92NXTwjndNXhklVNeOfZHdwNqqdiduVMtqsq/7QMo77Sh5GJhOWGVfb6rFJHFIIZv4pd5bsRAQ27AO+IiFjHVS2P1IygaapScdZvQziKlpoAvva+c3gvY0GyqZkYNE0r+U5epK6qDNbUbNRqIZKJiDQIZFQFcg9ge+5+RRt4x2D7MJVMI5FS4fNYH1QPC9hPBeCUmhE0TVUqlJohiBJZ3FAJRdEd7WakLkSqmGEwITJucXdV1r1VlPbuDKNqxq55OwJ2lwV0vxDT2balqQQXZfaWMutCWKSSbjMgIUIQJRLwutGRSaOYkZ45Ma6bXhfVVZb8WmZhNDWz2iPCUjPCRkTsNauKlppxuRTDQG2/X0asvWDCaDqpWl5NxhCx264ZkBAhCBNgJbxmVM70jk8BALoaxPGI2NXmnaVmRPOIsAhNLJFGMlNebCXZ7rJi7QNgfyRA1FLmGn82OmSXedcw7gq2F6VCQoQgTMCsyhlN04yISFe9gBERi8tXWeqnXrDUTE3OHagdkQDWpVe01AzAo4JITLOqy6Wgxs8qZ+zdC0rNEARxGoZhtcTUzPBEHNNJFYoCdNSJExFprLIrIiJm1YzbpRiVCnb0EmEHjmheGcDeRl6iD3mr5ZSyq6sQ6++jVEiIEIQJmBUR6R3T0zJttQFbKhLypd6uqhlBPSKAvYPvQoJ6RAB7q0Vyh7yJGAXI9lUpb+9QqYjzSUcQEmP0EsmU8BaLiGkZgINHRMBIALsLDdvQS8SomhFwH+yMiLCUR5XPDY+AQ96yfhl7PCIkRAiCmJPFDZVwKbqZcXgiXvTrnMgYVTsFMqoCQH1mAu/YZKIkobUQoqZmAPu8Eaqq5Rg0BdwHGyNDoncSZb4VO/YinkpjKjMINCigQC0FEiIEYQI+jwuL6jMlvCVUzvSOCRoRyQiDRErFZMKaUsVkWjVC8SKnZqz2iESnU2BaT8Q7XzvNqqLPVrEzNcP2W1FgmGSdAgkRgjAJ5hM5MjxR9Gv0stRMg1hCpNLnQcCrf1xY1UuEHfCKUt4HMGsjX+lzC+UTYjDTrj0RETErZhh2ljLn9hARbcxFqYh3lROEpKxsqQEAvDlUghDJmFW76sVKzQBZn4hVQoSlZYIVXmPar0iwQ8fyCcSCdlVlZGesWO+LED4iYqNfxqn+EICECEGYxsrWagDAwSKFSFrV0BdizczEiogAub1ELBIiAlfMAFlhYPWhExa4mRlgc2pGdI9IJjpkhygT2cBcKiRECMIkVrboQuTNwWhRz+8PTyGlavC6FaEG3jEaLO4lInLFDJATEbE8NcPufMVOR9jrERF0LyrtS81QRIQgiAVhqZm+8DSiRXwwsbTMoroKIVMT9TalZoSNiNhULRI2uqqKuQ92piNEnzZrZ0+VsOB7UQokRAjCJIKVXrTU6BNzDw8X3thMVKMqw+oJvCKX7gL2ddEUPQTP7sij8RTSqnWl3EDObBXyiFBEhCCI/GA+kUNFpGdOZEp3OwUr3WU0WDyBN+sREfODlkUorDarin7g5K6rmMhfIchTNWOjR0TQ66IUSIgQhImw9MyhIgyrIk7dzaXeaiFiRALEjIgYfoCppKVN3bKTd8U8cLxuFyp9bgB2lDILXjWTk5qx8poAsqJMVIFaCiRECMJEVrQUHxERtZkZI9vm3ZrDh0VEGgRNzbA70URaNTpcWkH2zlfMfQDs80YYU4gFFacsUpNWNcsa/TFEj5SVAgkRgjCRVa3FR0SOjepCZLGgHpHcNu9WkDWrivlBW+lzw5MxEVt5AIs8eZcRtKmXSFjwvajwuuF1W39N5L4+CRGCIOaFlfCeGJ/CZCL/D+mxWAIjmRk1LKoiGo1VuhHXqvLdkFG+K+bdr6IoxoFopU+EdVYV+cCxo4RX0zThjbuKotjYcVfslF0pkBAhCBOpr/KhqVo/SA8P5V85c2BAT+V0NVSgStA5EiwiMj6ZsKRaYkzwqhnAnsoZdviKLETs2IdYIo1U5joTOk1lkxChiAhBEHlj+ESG8veJHMx4SlZnUjsiwiIVqmb+h25a1YQPwwNZn4i1ERHx98GOqbPMH+LzuIw5RyJixzUBkBApmi9+8YvYsmULKisrUVdXZ+VbEYQwsMqZg4P5+0QOMCHSJq4Q8bpdxuE4mkkjmYVedaD/t6ipGSDXG2HNoTOdTCORUme8l4jYMewtlNNpV1HEa/DHsPqaAOS5LorFUiGSSCRw/fXX4+Mf/7iVb0MQQsHExBv9kbyfw1IzqwSOiABAYyZtMjJhrk+EGVVr/B543QLf/WZEEvNxmA07fN0uBdWCpugAezwiRoRM4LQMYP01AchzXRSLpb/RP//zPwMAfvjDH1r5NgQhFOs76wAAr/aGoGnagndzmqbh4ID4EREAaKz24/BwDKMxcyMiIQn8IYD1BzA7zOoq5IgC2OKVEThFBdgryoKCXxfFIpS0isfjiMezH3CRSP53lAQhCqvbauDzuBCeSuL46CSWNlXN+/j+8DSi8RQ8LgXLmsSsmGEwI+6oyRGRsZjYA+8YQYv9ALIcvqyPiJXpiPHJrCgTGauvCcDZ/hBAMLPqtm3bEAwGja+uri7eSyKIgvF5XDiroxYA8OqJ0IKPZ/6QZc1V8HmE+pM8DVbCa7ZHZFzwxlUMq+9+ZTlw7PBFyGBeBuyKDul/H04ceAcUIUTuueceKIoy79fOnTuLWsydd96JcDhsfPX29hb1OgTBG5ae2d0bWvCxsvhDgGzX01GTe4mMCd5VlWG5EJFknkjQhknEondVZdgxlTnrlxH7uiiWglMzt912G2688cZ5H7N06dKiFuP3++H3+4t6LkGIxDlddQB0n8hCGP4QCYSIVakZFmFhry8qVh86hkdE8MPXVo+I4Iev3R4RJ1KwEGlqakJTU5MVayEIx7A+I0Re74sgmVbnrQSRoXSX0VidSc2YbFZlVThN1WLfiFjtB5DlwDE8ItOpvAzZxSBDPxUAtnTbdfLAO8Bis2pPTw/GxsbQ09ODdDqN3bt3AwBWrFiB6mqxTXkEUQpLGytRG/AgMp3CgYEo1i4Kzvq4tKoZc2mkECJV1kREWHv7RsGFiOUREcmiAGlVQyyRtqSkNCzB8D/ApuiQw4WIpc64L3zhC9iwYQPuvvtuTExMYMOGDdiwYUPRHhKCkAVFUYyoyHw+kYODUSRSKip9bmGn7ubChMKIyWbVbERE7EOnNqeRl2pBm3tZogABrwu+TJTP+jSV2HsRzAglq64JQB7jbrFYKkR++MMfQtO0074uu+wyK9+WIISAGVZfm6dy5pmDwwCAC7ob4HKJ3x+ACYXIdMro9GgGWY+I2BERdkeqaUB02vzJs2FJIiKKomRnrFhdyiz4Xlh9TQBZIUJVMwRBFASLiPy1JzTnY545pAuRS1Y127Ci0qkNeOHJCKYxkypnVFUzXqtR8IiI3+NGhdcNwJpIgCzVQ4C182Y0TTOiQ6I3ufN5XKj06deEVd1VZfEOFQsJEYKwiPOW1MPtUvDm0ASODJ8+d2YykcLLR8cByCNEXC7FOBjMSs+Ep5LGlFXWp0RkDHOiBYcO66cigxCxct7MdFI1Im4ylKzaVdZNQoQgiIKor/LhLSv0CrNH9vSf9vMXj4whkVaxqK4CyxbovioSzLBqVkSEVeDUBjzCN3QDrDt0NE0z+rOIPPiPYeXhywSZ160Y0QaRsauaijwiBEEUzDvXtQMA/vu104XI9oPZtIxM8yOaTC7hHY5mjKo14kdDAOsOnclEdsKqTBERKzwiWX+IT4q/jWyUzJo0FaVmCIIomq1ntcLjUrB/IIo3h2amZ5g/5FJJ0jKMRpObmjFB0yRBWgawLhLAIkz+HM+ByNRbOHVWlooZhpXRoVgibaQuSYgQBFEwdZU+XLTy9PRM79gkjgzH4HYp2LKikdfyioL5OEZMEiIj0YwQqRE/CgBY10sk1x8iUxRg3IKIiCyt7hms10l40gLf0AyBKtScWtMgIUIQFvOOTHrmDznpmR88dxQAcO7iOqNLpSxkIyLmpGaYL0IGoypgfUREBn8IkBMRseDwlaWfCsPK2TsyGZiLhYQIQVjM1jPb4HUrODAYxVcfP4DHXh/AD58/BgD4+GXL+S6uCIx5MyaZVWVp786os+gAlu3AMSIiMWs9IjJgpVmVCVTR5w+VgjPjPAQhEMFKL+7Yuhr3Prof33zyTbgzfThuvqgbV5zRynl1hdOQiVyYFRHJtneX44O21qJDZywmR98MBjsYxy2JiJBHhMGus4YqOfaiGCgiQhA2cOuly7HtunVwKfp8jvVddfhfV53Be1lFwQSDWR4RWbqqMuotqpBgXoAGSQ7feguHvUnnEbGwaoYiIgRBmMb7Ny1GZ30FHnt9ALddsUKKnhmzwapbzOojIsucGUZDpbl9VBhjmciCLBERS6tmmBCRZC+M5m6WRESYQJVjL4qBhAhB2MjFK5tx8Uq5ynVPhUVEppJpTCZSJTv5ZYuINGR+/3GzhcgEM+3KceCwKMB0UsV0Mo2A17ySY5bukSYiUsF8QxZERJhAlSRSVgxy3pIRBMGNSp8bAa/+0VFqL5GpRBqxRBqAPB6RhhxvhJnTVmWLiFT7PcbcIbN9IrJ1ErW2y6xc3qFiICFCEERBKIqS00ukNMMqe77P40K1X44ALcvVq5q5B0/WIyLHgaMoimWVM0ZqRpaqmcw+TCXTiKfSpr72uGRl3cVAQoQgiIJhfo7haGlChJUAN1f7pWjiBeiiqSagi6YxEyMB45JFRADrSpllq5qp8XvALl/zG91RRIQgCOI0WmoDAIChEoUI66oqS1qG0WDy4D9V1YwDR5Y+IkDWt2Bmd9WpRBrTSX3mTlASIeJyKZbN3slGROTYi2IgIUIQRMG01uqpmaHIdEmvY8yZkcSoyjBbiESnU0hn/CayRAGAnIiIiZUz7JrwuhXUSJKuA6zxiWialo2UUWqGIAgiS2uNHhEZjJTqEZGrUoRhdgkvS/FU+z3we8QfeMeos6C5G9tTWWbuMKzYC91zIs9E5mIhIUIQRMG0ZlIzg9HSIiLMrNpUU94RkdzDVyaYb8HMUubsXsh1TRgdd800MGdEjc8tx0TmYiEhQhBEwbRkUjOlRkRGZY2ImHwAGwPvJNsHKybwjsXkvCasGAJo+EOqvFJFhwqFhAhBEAXDIiKlekQGM89vliwiUm9yRES29u4MKw5fWaNDhji1opLKwf4QgIQIQRBFwITIaCyBZFot+nUGMkKko67ClHXZhZGaMenQka2ZGSNbNWOmWVVOIVJv+IbMjw6RECEIgjiF+kovvG49VFxsLxFN0zAQ1oVIW0bYyILZZlXZmpkxslUzJh6+0qbrWHM380RZyOghIlekrFBIiBAEUTCKoqDFqJwpLj0TmkwaFQHMcyILbN6M2WZV2SIidRZM4DUiIpL1lqk3OUoGUESEIAhiXko1rPZnoiFN1T6pSlaBnHkzZkVEJuVOR4RMnLszlukjIl1ExIKpzCHyiBAEQcwN6yUyVGQJ70BkSn8dydIyQPbuN5ZIYzpZ+mwRWQ2aLCKianpTNjOQtXzXklLmMmjvDpAQIQiiSFqNiEiRQiSs3/m2B+UTIrUBcyfPytjeHQD8HrfR38Isw6qsZtXcqhmzokPZiAh5RAiCIE6DzZspNjUzENYjIm0SChFFUYy7VNYLpRRGM43dZAzB15toWE2kVCOyIltqJjc6FJk2xzMjq3eoUEiIEARRFK0lDr7rl7RihtFoUt+IREpFJHP4yhYFALIzVsyJDOmv4c4ZIicLfo8b1ZnZOGb5RIyqGQkFaiGQECEIoihKHXzHeoi0BeXqIcKoN8mcyNrce92KMa9EJlhpqRlNzVh0qb7SC5dLvk6ibC/MSlONSVrWXSgkRAiCKIpSy3dZDxEZPSKAefNmWB+Wpmq/lIdvnVFBVHo6QvZyVWawNaOp2XQyjamMEbqO+ogQBEGcDouIjE8mEU8VXjnChIiMVTOAefNmmBCRrc09o77SvIjImKRlzAzWot+MyhkWVfG4FNRkUj5OhYQIQRBFEazwwufRP0KGCjSsTsRTiMZ1X4SMZlUgayAcLVWIZFIzLdIKEeaVMSEiktmLRsmamTHMbGrGIkx1lT5HD7wDSIgQBFEkiqJkfSIF9hJh0ZCagMcw+MmGWWZV2SMiZppVZe2nwjCz0V22yZ2z0zIACRGCIErAaGpWYERE1hkzuZg1gdcQItVyChEWvTBDiIxK2syMYeZUZmZillWUFQIJEYIgiqa1tjjDar/EPUQYjWYLEUkjIk0ZATUSNS8iIlsPEUaDSVEyABjJVBA1SSpQC4GECEEQRcPmzfQXKESYcJG1YgYwb+w7S2vJKkQaM9ELdgdfCrJ2VWWYVdINZPeThAhBEMQ8dNZXAgBOjE8V9DyjmZmkPUSAmSmJdAktvZlZVVYh0lSTNWiWsg+AkyIipRt3ZY+UFQIJEYIgimZxgy5EescmC3qeEzwijVU+KAqQVrWi74A1TcvxiMi5Fw2V+j5oWumRAMOsKmnVDDOWmhkRkdU7VAiWCZFjx47hox/9KLq7u1FRUYHly5fj7rvvRiJh3mRCgiD4woTI8dEChYgDUjMet8u4cy92AvFEPIXppApA3jtfj9tlpCRKSc+kVS2nUkROIcL2ITyVRCqtlvRaRmqmRs69KATL6ub2798PVVXx3e9+FytWrMDrr7+OW265BbFYDF/5yleseluCIGykq0FPrYSnkghPJhHMc0qoERGRWIgAenfZkYkEhqJxnFXE81k0pMbvQUVmiq2MNFX7MBZLlDQAMDSZgJbJ7MjaWTVY4TWiQ6GpZEn+Dmb+LQePiGVC5KqrrsJVV11l/HvZsmU4cOAA7r//fhIiBOEQKn0eNFX7MTIRR+/4JIKVwQWfE51OGqbERfXyekQA3az7Rj8wXOQEYqf4AJqq/Tg4OFFSRISlM4IVXnjdcroGPG4XghVehCaTGIslihYRqqphNEZmVUsIh8NoaGiY8+fxeByRSGTGF0EQYrM4ExXpydMnwtI4TdU+1AbkbtbEuqEWO29n2Ai/y33YGCW8JQiRUcmNqowGEypnwlNJJNN6eEjWLrOFYJsQOXz4ML75zW/i1ltvnfMx27ZtQzAYNL66urrsWh5BEEXCfCL5CpEjIzEAQHdTlWVrsgs2+G8oWtwBzBrByR4RYYflSAmpGWP4n+R7UW/CDCIm6IIVXvg98qbs8qVgIXLPPfdAUZR5v3bu3DnjOX19fbjqqqtw/fXX4+abb57zte+8806Ew2Hjq7e3t/DfiCAIW1ncqAuKfIXI0WFdiCxtdIAQKbLFPWPYIZURZkREmJiTdeYOw+glUkJTMyNSVgbREKAIj8htt92GG2+8cd7HLF261Pjvvr4+XH755di8eTO+973vzfs8v98Pv1/ui5Agyo1CS3iPjWYiIs0OECIlRkSc4hFpNkOIROSexsxgJbylRUTKx6gKFCFEmpqa0NTUlNdjT548icsvvxwbN27EAw88AJdLTgMSQRBzU2xqZpkTUjMsIlLmZlWWmimlambQECJy70V23kzxTc2ckqbKF8uqZvr6+nDZZZdh8eLF+MpXvoLh4WHjZ21tbVa9LUEQNsOEyMnxKaTSKjzzVDxomoajwxMAgKVOECKZg2I4GoemaQWPax92SDrC3NSM5BERw6xa/F6UUzMzwEIh8vjjj+PNN9/Em2++ic7Ozhk/07TS2gATBCEOLTV++DwuJFIq+sPT6MoIk9kYn0wiMp0C4AyPCItkJNIqQpNJ4244X2Rv785gd+6jE4miBBmQjYi0SB4RaTREWQmpGYdEyvLFslzJhz/8YWiaNusXQRDOweVS0FWfXwnv0RE9GtIRDCDglb8awO9xoy7TxK1Qn0ha1TDqECHCSm4TadUQmoXC0luye0RYdKtYAzOQO/CuPMyqZNogCKJk8vWJHB3Rf+4Eoyqj1TCsFnbwjMbiUDXApWQn2MpKwOtGjV8PsBeTnplMpBCN6wJG9jRVtpKq+NTMcBlN3gVIiBAEYQL5CxE9IuKEHiIMdvAMFmhYZf6Qhio/3K7CUxmiwdIzI0UcwCwaUulzo9pvmWPAFpgwDU0mEU+li3oN1t5d9khZvpAQIQiiZLryFiLO6SHCaC4yFM/m7cheJcJgaYTRIspWB3NKd4vxl4hEXaUXvoxhe7gIUaZp5dXeHSAhQhCECbCICGtWNhcsNbPMQakZo5dIgRGRk6EpAMCiOrnn7TBYeqmY1IxTmpkBgKIoOeK08L0ot/buAAkRgiBM4MyOWgDAwcEoppOzh6NVVcMxo717tW1rs5rcEt5CODGuC5HO+rmrjGSCjasvJjWTrZiR26jKMIRIEf1l2HVUG/CURXt3gIQIQRAmsKiuAk3VPqRUDW/0zz6scjA6jalkGm6Xgk7Jp+7mwqo8Ck3NnMwIEdknEDOMXiJFpGZY5KDVARERIFecFl4545RBiIVAQoQgiJJRFAXrO+sAAK/2hmZ9zP7+KABgSWOltGPeZ6NYs+qJcT1N5RRRZvTPKMqs6oz27oxSKmdY/5FyaWYGkBAhCMIk1nfVAZhbiOw4OgoAOG9JvU0rsofcvhGF9Elymkek2ZjAW0xqJuMRcYhxt1jfEJAVchQRIQiCKBBDiJwIz/rzl46OAQAu6G60a0m2wA6d6aRq9MJYiKlE2rjz7XKKRyRzB19U1UwmhSF7e3cGE6eDJaRmKCJCEARRIOs7gwD0Et3QKSPQJxMp7MkIlE3dDbavzUoqfG7UBPTeF/neAbNoSI3fg9oKuftmMJgQYXN3CmHY6KrqjMO3lGGIg2FntLovBBIiBEGYQl2lD0sb9bv7106Jivz1eAgpVUNHMOAYT0QuzNvAeoMsBPOHLKqvkL5vBqMtqO/BZCKNyFT+bd5j8Zyuqk7xiBjddgsXIk5L2eUDCRGCIExjLp/ISxl/yAXLGh1z8ObC+qgcH5u/jwqDHTZOEmUBr9toanYiNH9ju1zYYV3lgK6qDBbNGI3FkUqrBT23L0xChCAIomiMyplTIiI7Mv4Qp6VlGEaL+9H8DmDWQ8Rph01H5vfpC+XvjXBaxQygN3dzKYCmFeaZSauaEVXrcNi1MR8kRAiCMA0WEdndGzJ8AtPJNHZnIiQXOFSILMmkpI7nKUROOqyZGaMjyITIVN7PGXTgyHu3SzE8M4X4REYm4kimNbgUZ3SZzRcSIgRBmMZZHbXwe1wYmYjjqQNDAPQ0TSKloqna76hhd7kwIXJsNL/UTK5HxEmw36cQIeLEiAiQ20sk/+gQS9m11QbgcVCvnYUon9+UIAjLCXjd+PCWpQCAL/5hHxIpFT947igAPRriRH8IACzJDPHrGZvMq2LEiR4RIJtOOFGAEHHa8D9GMYZVJuDKKS0DkBAhCMJkPnH5CjRU+XB4OIbrv/sCHn9jED63C7dcsoz30iyjs74CiqJXjLD+IHMRT6WNBl5O84gsqtMP30IiIsczE5uZz8YptBQxb4aECEEQhAkEK7z4h7euBJCtnvnXd6/FORn/iBPxe9yGP+L4AumZ/oyRs8LrRkOVs6arLqrTxUQhQoQZfBc3Oittl9txN1+YyZeECEEQRIm8f9NirGjRJ+x+5C3deN95XZxXZD35GlZP5Ay7c1qqqqMum45IpBYuW9U0DT0OjYg01xafmmGRpXLBGUXbBEEIhcftwo8+sgl/PT6Ot69r570cW1jSWInnD48aqYa5OBly1rC7XBqqfPB7XIinVAyEp7G4cX5xMTwRx1QyDZfivDRVNiJSgBAJU2qGIAjCNBbVVeCa9R1wu5x11z8Xixv01MJCqRkWMXHawQvoU5jZ73Uyj/QMS8t01FXA53HWcZT1iFBqZiGc9X+eIAiCE0vzTM3sH4gCAFa31Vi+Jh6wEt58hAjbqyULRE5khAmywch0XmmqqUQaY5nmZyRECIIgiIJhaYieBVIzb/RFAABnttdaviYeFNLUzKkVM4DeoK3C64aq5SfKWFqm2u9BbaC8XBMkRAiCIEyA9RIZiyUQmU7O+pixWAIDmVD9GU4VInX5C5GeTBqLpbWchKIoBTW6y5buBhxnYl4IEiIEQRAmUO33GEPf5po5s69fj4Ysaax0zIC3UykkNcOiR05MzQA5lVQjhQiR8krLACRECIIgTMOYwjuHEHF6WgbIlvAWIkScmJoBgKWZKNlClVQAcLJMjaoACRGCIAjTYOmZoyMTs/6cRUScLEQW5aRm5mt3PxFPGV1oFyrzlZXFBQxDzPYQISFCEARBFAkTGGza8Km8kREiaxwsRNqCekRkOqlifHJ2rwyQTV/VV3pRG/Dasja7YRGRfDwi/RmzanuwvJqZASRECIIgTGNTdwMA4KWjY0irM6MB8VQabw7pkZIzO5wrRPwet9FDo3eelISRlnFYa/dcmEekd2zytOvhVFjUpLPemdGh+SAhQhAEYRJnddSiyudGZDqFA5l+IYxDgxNIqRqCFV7H3/Uub9bb+x8YjM75mJ4xPUqwxKH+EABoD1bA53YhmdaMiMdsTMRTRuv/lZnRCOUECRGCIAiT8Lhd2LhUj4q8eHR0xs/eyPGHOL0886xMxIeZc2eDRQCcalQFALdLQWcDG4Y4d3ToYEawtdT4Ue+wQYj5QEKEIAjCRC7ISc/kYlTMODgtwzgzDyGSTc04V4gA+flEDjq82+5CkBAhCIIwkVyfSG7VyK6ecQDONqoyDCHSH4E6izdC0zSjgoilcZxKPlOZWQprdSsJEYIgCKJEzu4Mwu9xYTSWwOFh3Zz6+skwXj0Rhtet4JJVTZxXaD3Lm6vh87hmeB9y6R2bwshEAl63YqRxnIrRS2SeiAjzE62iiAhBEARRKn6PGxsW1wEAXsykZ370/DEAwNvXtaOlxtlGVQDwul3G3f3evvBpP3+lR9+XtYuCCHjdtq7NbvLpJcI8ImeQECEIgiDM4ILuRgDAH/cOYjgax+9e7QMA/N3mpRxXZS+spwoz6eby1+MhAMC5i+vtXBIXcj0iszV4G5mIY2QiAUUBVpRhxQxAQoQgCMJ03rqmFQDwzMFhvPObzyKRUrF2US3OzURKyoGzFs1tWP1rxi9TDkJkUV0F3C4F00kVQ9H4aT9nRtXFDZWo9Dlz/tBCkBAhCIIwmXWdQXz7A+fC73FhMKIfPjdtXur4st1cWERk7ylCJBZPYX/m8D13SZ3dy7Idn8dl9EqZLU1V7kZVgIQIQRCEJbzj7Hb84mOb0Vrrx5LGSlyzvoP3kmzljPZaKAowEJnG6EQ2EvDqiRDSqoaOYADtwfKYq8IqqV44PHraz5g/pFxLdwGLhcjf/u3fYvHixQgEAmhvb8eHPvQh9PX1WfmWBEEQwnBOVx2e+V+X40+3X+p4U+apVPs9hj9iX3+2w+qunhAAYMMS56dlGJuX656hF46cLkSMihmKiFjD5Zdfjl/+8pc4cOAAfvOb3+Dw4cN473vfa+VbEgRBCIXf44bXXZ7BZ5aeye0y+9fj5eMPYWxepguRvX0RhCYTxvc1TcPBQb3Eu1wrZgCLhcg//MM/4MILL8SSJUuwZcsWfO5zn8OOHTuQTM49kZEgCIJwBn+ztg2AXr4cmU4ilVZzjKp1HFdmLy21ASxvroKmZUu6AeD1kxFMxFPwe1xY2uTc4X8LYZtMHxsbw09/+lNs2bIFXu/sI5/j8TgikciML4IgCEJO3rGuHStaqhGZTuGB547h3/90EOOTSdQGPDirI8h7ebayZbneyC7XJ/Kbv54AALztzNayjZoBNgiRf/zHf0RVVRUaGxvR09OD3/3ud3M+dtu2bQgGg8ZXV1eX1csjCIIgLMLtUvD3V64EAHxn+2F8+6nDAIAvXbcOPk95HbyGTyQjRBIpFb/bfRIA8N6NndzWJQIFXwn33HMPFEWZ92vnzp3G4z/72c9i165dePzxx+F2u/F3f/d3szZ1AYA777wT4XDY+Ort7S3+NyMIgiC484517VjVWo2pZBoA8KELl+CdZ5dXBREAXJjxiRwYjGJ0Io6nDgxhfDKJlho/Ll7ZzHl1fCm4e8ptt92GG2+8cd7HLF261PjvpqYmNDU1YdWqVVizZg26urqwY8cObN68+bTn+f1++P3+QpdEEARBCIrLpeCOravxsf/7CtYtCuKud6zhvSQuNFT5cEZbDfYPRPH9544ajczefe4iuF3l019mNgoWIkxYFAOLhMTjp3eXIwiCIJzJ35zVhj98+iJ0N1WVXRlzLtes78D+gQO4/+nDxvfee255p2WAIoRIvrz00kt46aWXcNFFF6G+vh5HjhzBF77wBSxfvnzWaAhBEAThXMrNnDobH790ORqqfPjyY/sxPpnE+q46rCzj/iEMy4RIRUUFHnroIdx9992IxWJob2/HVVddhQcffJDSLwRBEETZ4XIpeP+mxXj72nb8954+XFLm3hCGos3lHBWASCSCYDCIcDiM2tpa3sshCIIgCCIPCjm/y6t+iiAIgiAIoSAhQhAEQRAEN0iIEARBEATBDRIiBEEQBEFwg4QIQRAEQRDcICFCEARBEAQ3SIgQBEEQBMENEiIEQRAEQXCDhAhBEARBENwgIUIQBEEQBDdIiBAEQRAEwQ0SIgRBEARBcIOECEEQBEEQ3PDwXsB8sMHAkUiE80oIgiAIgsgXdm6zc3w+hBYi0WgUANDV1cV5JQRBEARBFEo0GkUwGJz3MYqWj1zhhKqq6OvrQ01NDRRFMfW1I5EIurq60Nvbi9raWlNf22nQXuUP7VX+0F7lD+1VYdB+5Y9Ve6VpGqLRKDo6OuByze8CEToi4nK50NnZael71NbW0oWaJ7RX+UN7lT+0V/lDe1UYtF/5Y8VeLRQJYZBZlSAIgiAIbpAQIQiCIAiCG2UrRPx+P+6++274/X7eSxEe2qv8ob3KH9qr/KG9Kgzar/wRYa+ENqsSBEEQBOFsyjYiQhAEQRAEf0iIEARBEATBDRIiBEEQBEFwg4QIQRAEQRDcKEshct9996G7uxuBQAAbN27Es88+y3tJQnLPPfdAUZQZX21tbbyXJQTPPPMMrrnmGnR0dEBRFPz2t7+d8XNN03DPPfego6MDFRUVuOyyy7B3714+i+XMQnv14Q9/+LTr7MILL+SzWI5s27YN559/PmpqatDS0oJ3vetdOHDgwIzH0HWVJZ/9omtL5/7778fZZ59tNC3bvHkzHn30UePnvK+rshMiv/jFL/CZz3wGd911F3bt2oWLL74YV199NXp6engvTUjOOuss9Pf3G1979uzhvSQhiMViWL9+Pb71rW/N+vMvf/nL+NrXvoZvfetbePnll9HW1oa3ve1txvykcmKhvQKAq666asZ19sgjj9i4QjHYvn07PvnJT2LHjh144oknkEqlsHXrVsRiMeMxdF1lyWe/ALq2AKCzsxP33nsvdu7ciZ07d+KKK67Atddea4gN7teVVmZs2rRJu/XWW2d874wzztA+97nPcVqRuNx9993a+vXreS9DeABoDz/8sPFvVVW1trY27d577zW+Nz09rQWDQe073/kOhxWKw6l7pWmadtNNN2nXXnstl/WIzNDQkAZA2759u6ZpdF0txKn7pWl0bc1HfX299v3vf1+I66qsIiKJRAKvvPIKtm7dOuP7W7duxfPPP89pVWJz6NAhdHR0oLu7GzfeeCOOHDnCe0nCc/ToUQwMDMy4zvx+Py699FK6zubg6aefRktLC1atWoVbbrkFQ0NDvJfEnXA4DABoaGgAQNfVQpy6Xwy6tmaSTqfx4IMPIhaLYfPmzUJcV2UlREZGRpBOp9Ha2jrj+62trRgYGOC0KnG54IIL8OMf/xh//OMf8R//8R8YGBjAli1bMDo6yntpQsOuJbrO8uPqq6/GT3/6Uzz55JP46le/ipdffhlXXHEF4vE476VxQ9M03H777bjooouwdu1aAHRdzcds+wXQtZXLnj17UF1dDb/fj1tvvRUPP/wwzjzzTCGuK6Gn71qFoigz/q1p2mnfI/Q/Ysa6deuwefNmLF++HD/60Y9w++23c1yZHNB1lh833HCD8d9r167FeeedhyVLluAPf/gDrrvuOo4r48dtt92G1157Dc8999xpP6Pr6nTm2i+6trKsXr0au3fvRigUwm9+8xvcdNNN2L59u/FzntdVWUVEmpqa4Ha7T1N5Q0NDp6lB4nSqqqqwbt06HDp0iPdShIZVFtF1Vhzt7e1YsmRJ2V5nn/rUp/D73/8eTz31FDo7O43v03U1O3Pt12yU87Xl8/mwYsUKnHfeedi2bRvWr1+Pb3zjG0JcV2UlRHw+HzZu3IgnnnhixvefeOIJbNmyhdOq5CEej2Pfvn1ob2/nvRSh6e7uRltb24zrLJFIYPv27XSd5cHo6Ch6e3vL7jrTNA233XYbHnroITz55JPo7u6e8XO6rmay0H7NRrleW7OhaRri8bgY15UtlliBePDBBzWv16v94Ac/0N544w3tM5/5jFZVVaUdO3aM99KE44477tCefvpp7ciRI9qOHTu0d77znVpNTQ3tlaZp0WhU27Vrl7Zr1y4NgPa1r31N27Vrl3b8+HFN0zTt3nvv1YLBoPbQQw9pe/bs0d7//vdr7e3tWiQS4bxy+5lvr6LRqHbHHXdozz//vHb06FHtqaee0jZv3qwtWrSo7Pbq4x//uBYMBrWnn35a6+/vN74mJyeNx9B1lWWh/aJrK8udd96pPfPMM9rRo0e11157Tfv85z+vuVwu7fHHH9c0jf91VXZCRNM07dvf/ra2ZMkSzefzaeeee+6Mci8iyw033KC1t7drXq9X6+jo0K677jpt7969vJclBE899ZQG4LSvm266SdM0vdTy7rvv1tra2jS/369dcskl2p49e/gumhPz7dXk5KS2detWrbm5WfN6vdrixYu1m266Sevp6eG9bNuZbY8AaA888IDxGLqusiy0X3RtZfnIRz5inHnNzc3alVdeaYgQTeN/XSmapmn2xF4IgiAIgiBmUlYeEYIgCIIgxIKECEEQBEEQ3CAhQhAEQRAEN0iIEARBEATBDRIiBEEQBEFwg4QIQRAEQRDcICFCEARBEAQ3SIgQBEEQBMENEiIEQRAEQXCDhAhBEARBENwgIUIQBEEQBDdIiBAEQRAEwY3/HxNlI/VeMovWAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an I/O system simulation to see what happens\n",
    "io_saturation = ct.NonlinearIOSystem(\n",
    "    None,\n",
    "    lambda t, x, u, params: F_saturation(u),\n",
    "    inputs=1, outputs=1\n",
    ")\n",
    "\n",
    "sys = ct.feedback(ct.ss(H_simple), io_saturation)\n",
    "T = np.linspace(0, 30, 200)\n",
    "t, y = ct.input_output_response(sys, T, 0.1, 0)\n",
    "plt.plot(t, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Limit cycle prediction with for a time-delay system with backlash\n",
    "\n",
    "This example demonstrates a more complicated interaction between a (non-static) nonlinearity and a higher order transfer function, resulting in multiple intersection points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<control.ctrlplot.ControlPlot at 0x11bebfe10>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Linear dynamics\n",
    "H_simple = ct.tf([1], [1, 2, 2, 1])\n",
    "H_multiple = H_simple * ct.tf(*ct.pade(5, 4)) * 4\n",
    "omega = np.logspace(-3, 3, 500)\n",
    "\n",
    "# Nonlinearity\n",
    "F_backlash = ct.friction_backlash_nonlinearity(1)\n",
    "amp = np.linspace(0.6, 5, 50)\n",
    "\n",
    "# Describing function plot\n",
    "ct.describing_function_plot(H_multiple, F_backlash, amp, omega, mirror_style=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
